The rainfall rate is a crucial variable in modeling runoff and water erosion. Rainfall rates present a very large spatial and temporal variability. Radars are used to estimate the spatial and temporal changes in rainfall rates during storms. The radar reflectivity is strongly affected by the drop size distribution (DSD) that results from the relative intensity of the microphysical processes involved in rainfall formation. One of the mathematical models applied to quantify the DSD is the Weibull function. Rainfall rate and kinetic energy, and radar reflectivity, are all related to different moments of the DSD. An analytical expression for these moments is proposed in the case of the Weibull distribution. The resulting relationships between radar reflectivity, rainfall rate, and kinetic energy are presented. The use of a scaled DSD that is independent of rainfall rate and characterizes a specific location allows an a priori estimate of relationships between radar reflectivity, rainfall rate, and kinetic energy that will be also characteristics of that location. Radar reflectivity can be used to estimate the kinetic energy of rainfall events. This extends the application of radar to agriculture and environmental purposes such as potential rainfall damages estimates in terms of soil loss, erosion, and sediment transport.

中文翻译：

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威布尔液滴尺寸分布引起的雷达反射率与降雨率和动能之间的关系

降雨率是模拟径流和水蚀的关键变量。降雨率存在很大的时空变化。雷达用于估计暴风雨期间降雨率的时空变化。雷达反射率受液滴大小分布（DSD）的强烈影响，该液滴大小分布是由与降雨形成有关的微物理过程的相对强度引起的。用于量化DSD的数学模型之一是Weibull函数。降雨率和动能以及雷达反射率都与DSD的不同时刻有关。在威布尔分布的情况下，提出了这些矩的解析表达式。给出了雷达反射率，降雨率和动能之间的关系。使用与降雨率无关并表征特定位置的缩放DSD，可以对雷达反射率，降雨率和动能之间的关系进行先验估计，这也是该位置的特征。雷达反射率可用于估算降雨事件的动能。这将雷达的应用范围扩展到农业和环境目的，例如根据土壤流失，侵蚀和泥沙输送估算潜在的降雨破坏。